Question

Find the value of each variable. Line / is a tangent

Answer 1

Answer:

a° = 118° , b° = 49° , c° = 144° , d° = 98°

Step-by-step explanation:

* Lets study the figure and take the information to solve the question

- There is a circle

- There is an inscribed triangle in the circle

- Each vertex of the triangle is an inscribed angle in the circle

- Each vertex subtended by an arc

- The measure of any inscribed angle is half the measure of its

  subtended arc

* Now lets solve the question

- The sum of the measures of the interior angles of a triangle is 180°

∵ The triangle has angle of measure 59° and another angle of

   measure 72°

∴ The measure of the third angle = 180° - (59° + 72°) = 49°

∵ b° is the measure of the third angle in the triangle

∴ b° = 49°

- The arc of measure a° is intercept the angle of measure 59°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 a° = 59° ⇒ multiply both sides by 2

∴ a° = 118°

- The arc of measure c° is intercept the angle of measure 72°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 c° = 72° ⇒ multiply both sides by 2

∴ c° = 144°

- The arc of measure d° is intercept the angle of measure 49°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 d° = 49° ⇒ multiply both sides by 2

∴ d° = 98°